g Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 76 and 124? (b) What percentage of people has an IQ score less than 64 or greater than 136? (c) What percentage of people has an IQ score greater than 136?

a) 95% of people has an IQ score between 76 and 124.

b) 0.3% of people has an IQ score less than 64 or greater than 136.

c) 0.15% of people has an IQ score greater than 136

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 100

Standard deviation = 12

(a) What percentage of people has an IQ score between 76 and 124?

76 = 100 - 2*12

124 = 100 + 2*12

So within 2 standard deviations of the mean, and the percentage is 95%.

(b) What percentage of people has an IQ score less than 64 or greater than 136?

64 = 100 - 3*12

136 = 100 + 3*12

99.7% of people has scores between 64 and 136. So 100 - 99.7 = 0.3% of people has an IQ score less than 64 or greater than 136.

(c) What percentage of people has an IQ score greater than 136?

0.3% of people has an IQ score less than 64 or greater than 136.

Since the normal distribution is symmetric, 0.3%/2 = 0.15% are below 64 are 0.15% are above 136.

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